Notes

In many physical situations effects become decreasingly important as they propagate further away. But in active or excitable media such as heart, muscle and nerve tissue an effect can maintain its magnitude as it propagates, leading to the formation of a variety of spatial structures. An early model of such media was constructed in 1946 by Norbert Wiener and Arturo Rosenblueth, based on a discrete array of continuous elements. Models with discrete elements were already considered in the 1960s, and in 1977 James Greenberg and Stuart Hastings introduced a simple 2D cellular automaton with three colors. The pictures below show what is probably the most complex feature of this cellular automaton and related systems: the formation of spiral waves. Such spiral waves were studied in 2D and 3D in the 1970s and 1980s, particularly by Arthur Winfree and others; they are fairly easy to observe in both inorganic chemical reactions (see below) and slime mold colonies.